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This work presents a generalized Kirchhoff-Love shell theory that canexplicitly capture fiber-induced anisotropy not only in stretching andout-of-plane bending, but also in in-plane bending. This setup is particularlysuitable for heterogeneous and fibrous materials such as textiles,biomaterials, composites and pantographic structures. The presented theory is adirect extension of classical Kirchhoff-Love shell theory to incorporate thein-plane bending resistance of fibers. It also extends existing second-gradientKirchhoff-Love shell theory for initially straight fibers to initially curvedfibers. To describe the additional kinematics of multiple fiber families, aso-called in-plane curvature tensor -- which is symmetric and of second order-- is proposed. The effective stress tensor and the in-plane and out-of-planemoment tensors are then identified from the mechanical power balance. Thesetensors are all second order and symmetric in general. Constitutive equationsfor hyperelastic materials are derived from different expressions of themechanical power balance. The weak form is also presented as it is required forcomputational shell formulations based on rotation-free finite elementdiscretizations.

A general theory for anisotropic Kirchhoff-Love shells with in-plane bending of embedded fibers